Commuting times for employees of a local company have a mean of 63.6minutes and a standard deviation of 3 minutes. What does Chebyshev'sTheorem say about the percentage of employees with commuting timesbetween 56.1 minutes and 71.1 minutes?At most 84% of the commuting times should fall between 56.1 minutes and 71.1minutes.Approximately 84% of the commuting times should fall between 56.1 minutesand 71.1 minutes.At least 84% of the commuting times should fall between 56.1 minutes and 71.1minutes.At least 99.7% of the commuting times should fall between 56.1 minutes and 71.1minutes.

Given, μ=63.6 minutesσ=3 minutes Let X denotes the commuting times for employees of a local company. Therefore X~Nμ=63.6,σ=3 Chebyshev's theorem is given as- Pμ-kσ<X<μ+kσ>1-1k2 Using the Chebyshev's theorem, the probability of employees with commuting time between 56.1 minutes and 71.1 minutes is obtained as- P56.1<X<71.1=P63.6-2.5×3<X<63.6+2.5×3>1-12.52>0.84 Therefore, the percentage of employees with commuting time between 56.1 minutes and 71.1 minutes is at least 0.84×100=84% Thus, Option C " At least 84% of the commuting times should fall between 56.1 minutes and 71.1 minutes." is the correct option.

Math

Statistics

Commuting times for employees of a local company have a mean of 63.6 minutes and a standard deviation of 3 minutes. What does Chebyshev's Theorem say about the percentage of employees with commuting times between 56.1 minutes and 71.1 minutes?

Commuting times for employees of a local company have a mean of 63.6 minutes and a standard deviation of 3 minutes. What does Chebyshev's Theorem say about the percentage of employees with commuting times between 56.1 minutes and 71.1 minutes?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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